Winter Physical Systems: Quantum and Modern physics Dr. E.J. Zita, The Evergreen State College, 6.Jan.03 Lab II Rm 2272, Program syllabus, schedule, and details online at Monday: QM (and Modern Q/A) Tuesday: DiffEq with Math Methods and Math Seminar (workshop on WebX in CAL tomorrow at 5:00) Wed: office hours 1:00 Thus: Modern (and QM Q/A) and Physics Seminar TA?

Outline: Logistics Modern physics applies Quantum mechanics Compare Quantum to Classical Schroedinger equation and Planck constant Wave function and probability Exercises in probability Expectation values Uncertainty principle Applications… Sign up for your minilectures

Time budget Plus your presentations: * minilectures (read Learning Through Discussion and ML Guidelines) * library research (to prepare for projects in spring) Science Seminar: * Tues. Math seminar: Chaos and Humor * Thus. Physics seminar: Alice and Heisenberg

Quantum Mechanics by Griffiths Theory : careful math and careful reasoning Modern Physics by OHanian Applications: more numerical than theoretical

Links between QM and Modern From Tom Moore’s Unit Q

How can we describe a system and predict its evolution? Classical mechanics: Force completely describes a system: Use F=ma = m dp/dt to find x(t) and v(t). Quantum mechanics: Wavefunction  completely describes a QM system

Review of Modern physics basics Energy and momentum of light: Can construct a differential operator for momentum (more careful derivation in a few weeks)

Planck constant h = 6.63 x J.s Invented by Planck (1900) to phenomenologically explain blackbody radiation Planck derived h from first principles a few weeks later, treating photons as quantized in a radiating cavity Fundamental unit of quantization, angular momentum units Used by Einstein to explain photoelectric effect (1905) and Bohr to derive H atom model (1912)

Schroedinger eqn. = Energy conservation E = T + V E  = T  + V  where  is the wavefunction and energy operators depend on x, t, and momentum: Solve the Schroedinger eqn. to find the wavefunction, and you know *everything* possible about your QM system.

Wave function and probability Probability that a measurement of the system will yield a result between x1 and x2 is

Measurement collapses the wave function This does not mean that the system was at X before the measurement - it is not meaningful to say it was localized at all before the measurement. Immediately after the measurement, the system is still at X. Time-dependent Schroedinger eqn describes evolution of  after a measurement.

Exercises in probability: qualitative

Exercises in probability: quantitative 1. Probability that an individual selected at random has age=15? 2. Most probably age? 3. Median? 4. Average = expectation value of repeated measurements of many identically prepared system: 5. Average of squares of ages = 6. Standard deviation  will give us uncertainty principle...

Exercises in probability: uncertainty Standard deviation  can be found from the deviation from the average: But the average deviation vanishes: So calculate the average of the square of the deviation: Homework (p.8): show that it is valid to calculate  more easily by: 1.1 Find these quantities for the exercise above.

Expectation values Most likely outcome of a measurement of position, for a system (or particle) in state  :

Uncertainty principle Position is well-defined for a pulse with ill-defined wavelength. Spread in position measurements =  x Momentum is well-defined for a wave with precise . By its nature, a wave is not localized in space. Spread in momentum measurements =  p We will show that

Particles and Waves Light interferes and diffracts - but so do electrons! in Ni crystal Electrons scatter like little billiard balls - but so does light! in the photoelectric effect

Applications of Quantum mechanics Sign up for your MinilecturesMinilectures Blackbody radiation: resolve ultraviolet catastrophe, measure star temperatures Photoelectric effect: particle detectors and signal amplifiers Bohr atom: predict and understand spectra and energies Structure and behavior of solids, including semiconductors Scanning tunneling microscope Zeeman effect: measure magnetic fields of stars from light Electron spin: Pauli exclusion principle Lasers, NMR, nuclear and particle physics, and much more...